How can I use Visual Keys?
This is not employing Visual keys but these examples do allow you to switch freely between constraints, animation and physics. Something akin to this - Rigidbody - Change Dynamic simulation to animatic -

Go to the link at bottom and at the bottom of that answer again there is a demo, switching from animated and physics and back again, along with a path constraint thrown in for good measure.

You can use model duplication or if the model is complex, use a 'Child-of' constraint's influence slider as described along the way.

Additionally a path constraint can be departed from mid-length as shown here (the 2nd path wouldn't be needed) - 

How to sequence paths? 

If the path has been followed to the end, it's constraint will become ineffective anyway. The model can be freely animated. 

Another alternative is to bake the constraint action to keyframes and after deleting any redundant Dopesheet strips, the model is again free to do as you wish. Make sure to tick all boxes in the bake panel.

I've thrown this together in a hurry as it's quite late and will elaborate if you need more detail.